Optimization-Based System Identification and Moving Horizon Estimation Using Low-Cost Sensors for a Miniature Car-Like Robot

TL;DR

Chronos presents a low-cost, open-source miniature car-like robot and a complete optimization-based pipeline for system identification, state estimation, and control using low-cost sensors. A modified AWD bicycle model with Pacejka tire forces and a low-velocity slip extension enables accurate dynamics across all speeds, while a gamma-based AWD split and a Taylor-like friction term capture drive-train and resistive effects. The workflow combines offline optimization (FIE) for parameter identification, online moving horizon estimation (MHE) for robust state tracking, and model-predictive contouring control (MPCC) for high-performance path tracking, all validated through extensive hardware experiments and released under BSD-2-Clause. The resulting framework delivers accurate open-loop predictions (RMSE down to $0.09$ m over $2$ s) and robust closed-loop performance even during sensor dropout, providing a practical benchmark for nonlinear identification, estimation, and model-based control in education and research.

Abstract

This paper presents an open-source miniature car-like robot with low-cost sensing and a pipeline for optimization-based system identification, state estimation, and control. The overall robotics platform comes at a cost of less than \$\,700 and thus significantly simplifies the verification of advanced algorithms in a realistic setting. We present a modified bicycle model with Pacejka tire forces to model the dynamics of the considered all-wheel drive vehicle and to prevent singularities of the model at low velocities. Furthermore, we provide an optimization-based system identification approach and a moving horizon estimation (MHE) scheme. In extensive hardware experiments, we show that the presented system identification approach results in a model with high prediction accuracy, while the MHE results in accurate state estimates. Finally, the overall closed-loop system is shown to perform well even in the presence of sensor failure for limited time intervals. All hardware, firmware, and control and estimation software is released under a BSD 2-clause license to promote widespread adoption and collaboration within the community.

Figures (8)

• Figure 1: (a) Chronos car based on a Kyosho AWD buggy model with custom electronics: IMU, wheel encoders with magnets in wheels, and Lighthouse positioning deck. (b) Track setup with Lighthouse base station. (c) Hardware experiment.
• Figure 2: The left figure demonstrates a single sweep of the light plane by the base station. Both light planes rotate around the $z$-axis. The second light plane is rotated by 60° compared to the first plane (depicted here in blue). The right image demonstrates the angles measured by the onboard sensors. The angles $\alpha_{1,1}$, $\alpha_{2,1}$ refer to the angle measurement of the first and second sensor for the first light plane sweep.
• Figure 3: Dynamic bicycle model with velocity in direction of each wheel used for the wheel encoder model (adapted from Froehlich2022).
• Figure 4: Left: Reprojection error (scaled $30\times$) of calibration points. Right: Mean/maximum calibration residual by number of points.
• Figure 5: Open-loop predicted trajectories from inputs $\{\tilde{u}_j \}_{j=t}^{t+M}$ based on the prior parameter estimate $\bar{\theta}_0$ and posterior identified system model $\hat{\theta}$.